You are inside the Great Hall, 15 m from the north wall with the doors to the RMC, and centered between two open doors that are 3 m apart. Someone is blairing a 200 Hz tone outside the Great Hall so that it enters the doors as a plane wave. You hear a maximum intensity in your current position. As you walk along the direction of the wall with the doors (but maintain a distance 15 m from the wall), how far will you walk (in m) to hear a minimum in the sound intensity

Δr = 0.425 m

Explanation:

This is a sound interference exercise, the expression for destructive interference is

          Δr = (2n + 1) λ / 2

in this case the movement is in the same direction as the sound, therefore the movement is one-dimensional

let's use the relationship between the speed of sound and its frequency and wavelength

          v = λ f

          λ = v / f

the first minium occurs for n = 0

           Δr = λ / 2

            Δr = v / 2f

            Δr =

             Δr = 0.425 m

this is the distance from the current position that we assume in the center of the room